How much was atheism frowned upon? Were there any punishments?
The term atheism was used in a different way in Ancient Rome so it might skew the results of how common it was.
As it was regarded as anything that deviated from the beliefs sanctioned by the state, thus anyone who did not believe in the gods approved by the state was deemed an atheist. This made Christians technically atheist towards the states beliefs and liable to face capital punishment. (Whitmarsh, Battling the Gods: Atheism in the Ancient World)